First, we can note that, whatever these three angles are, their sum is going to give us 180°, since we're talking about the interior angles of a triangle.
What this 3-way ratio is telling us is that, if we split that 180° up into some number of equal-sized pieces, the first angle will take up 2 pieces, the second one will take up 3, and the third one will take up 4. But how do we know the number of pieces that 180° was split up into in the first place? Well, we know we've got 2 pieces, 3 pieces, and 4 pieces, so putting those together gets us a total of 2 + 3 + 4 = <em>9 pieces! </em>
How big are each of those pieces? If we split 180 up into 9, we find that they're each 180 ÷ 9 = <em>20°</em>. This means that 2 pieces will be 20 x 2 = 40°, 3 pieces will be 20 x 3 = 60°, and 4 pieces will be 20 x 4 = 80°. So, our three angles are 40°, 60°, and 80°, making 40° the smallest of the three.
(We can check that this is correct by adding the angles together, finding that 40 + 60 + 80 = 100 + 80 = 180°, which is exactly what we wanted.)
